Method and apparatus for signal decomposition, analysis, reconstruction and tracking

ABSTRACT

A system and method for representing quasi-periodic (“qp”) waveforms, for example, representing a plurality of limited decompositions of the qp waveform. Each decomposition includes a first and second amplitude value and at least one time value. In some embodiments, each of the decompositions is phase adjusted such that the arithmetic sum of the plurality of limited decompositions reconstructs the qp waveform. Data-structure attributes are created and used to reconstruct the qp waveform. Features of the qp wave are tracked using pattern-ecognition techniques. The fundamental rate of the signal (e.g., heartbeat) can vary widely, for example by a factor of 2-3 or more from the lowest to highest frequency. To get quarter-phase representations of a component (e.g., lowest frequency “rate” component) that varies over time (by a factor of two to three) many overlapping filters use bandpass and overlap parameters that allow tracking the component&#39;s frequency version on changing quarter-phase basis.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority benefit, under 35 U.S.C. §119(e), ofU.S. Provisional Patent Application No. 61/801,292, filed Mar. 15, 2013,which is incorporated herein by reference in its entirety. Thisapplication is related to U.S. patent application Ser. No. 13/220,679,filed Aug. 29, 2011 (which issued as U.S. Pat. No. 8,386,244 on Feb. 26,2013), titled “SIGNAL DECOMPOSITION, ANALYSIS AND RECONSTRUCTION,” whichis a divisional of U.S. patent application Ser. No. 12/760,554, filedApr. 15, 2010 (which issued as U.S. Pat. No. 8,010,347 on Aug. 30,2011), titled “SIGNAL DECOMPOSITION, ANALYSIS AND RECONSTRUCTIONAPPARATUS AND METHOD,” which is a divisional of U.S. patent applicationSer. No. 11/360,135, filed Feb. 23, 2006 (which issued as U.S. Pat. No.7,702,502 on Apr. 20, 2010), titled “APPARATUS FOR SIGNAL DECOMPOSITION,ANALYSIS AND RECONSTRUCTION,” which claimed benefit of U.S. ProvisionalPatent Application 60/656,630, filed Feb. 23, 2005, titled “SYSTEM ANDMETHOD FOR SIGNAL DECOMPOSITION, ANALYSIS AND RECONSTRUCTION,” each ofwhich is incorporated herein by reference in its entirety. Thisapplication is also related to U.S. patent application Ser. No.11/360,223, filed Feb. 23, 2006 (which issued as U.S. Pat. No. 7,706,992on Apr. 27, 2010), titled “SYSTEM AND METHOD FOR SIGNAL DECOMPOSITION,ANALYSIS AND RECONSTRUCTION,” which is incorporated herein by referencein its entirety.

FIELD OF THE INVENTION

This invention relates to the field of computer-implemented systems andmethods, and more specifically a software-, embedded-circuits- orfirmware-implemented system and method to decompose signals havingquasi-periodic wave properties using high-resolution filter banks, toderive which filter band(s) contains the base signal of interest, tostore such signals in a data structure, analyze such signals, andreconstruct such signals from the data structure, and/or to transmitsuch data structure over a communications channel.

COPYRIGHT & TRADEMARK NOTICES

A portion of the disclosure of this patent document contains material,which is subject to copyright protection. The owner has no objection tothe facsimile reproduction by anyone of the patent document or thepatent disclosure, as it appears in the Patent and Trademark Officepatent file or records, but otherwise reserves all copyrightswhatsoever.

Certain marks referenced herein may be common-law or registeredtrademarks of third parties affiliated or unaffiliated with theapplicant or the assignee. Use of these marks is for providing anenabling disclosure by way of example and shall not be construed tolimit the scope of the claimed subject matter to material associatedwith such marks.

FIGS. 10, 11.1, 11.2, 11.3, 12, 13, 14, 15.1, 15.2, 15.1 and 15.2include source-code files that make up one embodiment of the presentinvention. These copyrighted source-code files are incorporated byreference in their entirety into this application. The owner has noobjection to the facsimile reproduction by anyone of the patent documentor the patent disclosure, as it appears in the Patent and TrademarkOffice patent file or records, but otherwise reserves all copyrightswhatsoever.

BACKGROUND OF THE INVENTION

The digital representation of waveforms is a technology that is centralto various sectors of industry where the detection of periodic andnon-periodic waveforms can be critical to determining whether an erraticheartbeat, electrical short circuit, or some other problem exists. Adigital representation must clearly and accurately represent the analogsource of a waveform, but at the same time be able to accomplish suchthings as, compressing the incoming data into some manageable size, andmaintain the integrity of the incoming data (i.e., making sure that thedigital representation has enough fidelity to the original signal to beuseful). Of additional import is the ability to have a digitalrepresentation that can consistently allow one to identify the presenceand location of certain wave features, and/or that lends itself tocertain types of automated analyses.

High-fidelity digital representations are problematic for a number ofreasons. First, they require relatively large amounts of space withinwhich to store the digitized data. Put another way, the higher thefidelity of the digitized data, the larger the amount of storage needed.Another problem with high-fidelity digital representations is that theycan result in large amounts of digital data that has little or no importin terms of conveying meaning. For example, a periodic wave signal thatmerely repeats the same waveform does not convey much meaning to theperson analyzing the waveform, and may in fact just take up storagespace with unremarkable data. An additional problem is the repeatedsampling, over sampling of such high-fidelity data even though it isotherwise unremarkable. Such over sampling results in wasted processingbandwidth (i.e., processor cycles, and/or power) as well as databandwidth (data storage space and/or transmission bandwidth).

U.S. Pat. No. 8,086,304 issued on Dec. 27, 2011, with the title“Physiologic signal processing to determine a cardiac condition,” and isincorporated herein by reference in its entirety. U.S. Pat. No.8,086,304 describes, that in a method for determining a cardiaccondition, a sensed physiologic signal for a period of time includingmultiple cardiac cycles is received. A plurality of harmonics of thereceived physiologic signal is extracted based on a reference frequency,wherein the harmonics correspond to a plurality of alternansfrequencies. Amplitudes of at least some of the extracted harmonics aredetermined, and are used to determine an alternans indicator value.

What is needed is a method and structure that efficiently and accuratelycaptures the underlying waveform, with little or no degradation of thevalue and meaning of that waveform data. In particular, what is neededis a method and apparatus that tracks and records the properties of aparticular frequency component of a complex waveform.

BRIEF SUMMARY OF THE INVENTION

In some embodiments, the present invention provides a method andapparatus that tracks and records a particular frequency component(e.g., the rate and amplitude of the lowest frequency of, for example, aheart beat of an electrocardiogram (ECG) signal) as that frequencycomponent changes frequency over a wide range of frequencies.

In some embodiments, the present invention provides a method andapparatus that tracks and records the properties of a particularfrequency component, such as the component corresponding to thetime-local fundamental period of a quasi-periodic waveform (e.g., therate and amplitude of the frequency component corresponding to, forexample, the local cardiac cycle length of an electrocardiogram (ECG)signal, or a seismic signal) as that frequency component varies infrequency over a wide range of frequencies. Some embodiments provide amethod and apparatus that perform digital filtering using a plurality ofbanks of filters whose frequency ranges overlap and whose centerfrequencies are closely spaced, and performing wavelet transforms onfrequency components detected in the filtered signals from the pluralityof banks of filters, and then tracking the components with the strongestsignal within one of the overlapping filter banks (such that aparticular frequency component that changes frequency over time can betracked as its frequency shifts to higher or lower frequencies), inorder to track that component as its frequency or period changes over alarge range. In some embodiments, changes in frequency of up to 2:1 or3:1 or more can be tracked. For example, a human heartbeat can oftenvary from fifty beats per minute (50 BPM, or even as low as 30 BPM orless) to two-hundred beats per minute (200 BPM or even 300 BPM or more).In some embodiments, the present invention tracks a component of thecardiac signal over a range of about thirty beats per minute or less tothree-hundred beats per minute or more (a range of 5:1). In someembodiments, the present invention tracks each of a plurality offrequency components of such a varying heartbeat, wherein each of thecomponents shifts in frequency as the BPM rate changes.

In some embodiments, the present invention includes a system and methodfor representing quasi-periodic (“QP”) waveforms. For example, in someembodiments, the method includes representing each of a plurality oflimited decompositions as a QP waveform. Each QP decomposition includesa first and second amplitude value and at least one time value. In someembodiments, each of the decompositions is phase adjusted such that thearithmetic sum of the plurality of limited decompositions reconstructsthe QP waveform. Data-structure attributes are created and used toreconstruct the QP waveform. Features of the QP wave are tracked usingpattern-recognition techniques. The fundamental rate of the signal(e.g., heartbeat) can vary widely, for example by a factor of 2-3 ormore from the lowest to highest frequency. To get quarter-phaserepresentations of a component (e.g., lowest frequency “rate” component)that varies over time (by a factor of two to three) many bandpassfilters are arranged with closely-spaced center frequencies to providetracking of the component's frequency variation on a per-quarter-phasebasis. Some embodiments provide tracking of the component's frequencyvariation on a per-digital-sample basis.

Accordingly, one aspect of the present invention provides a method andapparatus that tracks and records a particular frequency component(e.g., the rate and amplitude of the lowest (i.e., fundamental)frequency of, for example, the cardiac cycle of an electrocardiogram(ECG) signal) as that frequency component changes frequency over a widerange of frequencies.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1.1 is a block diagram of a parallel filter bank system 100,according to some embodiments of the present invention.

FIG. 1.2 is a block diagram of a system 2300 of an input/analysisprocess 2301, an interpretive process 2305, a storage/transmission block2309, and a re-synthesis/output process 2310, according to someembodiments of the present invention.

FIG. 2 is a block diagram of a subsystem 2400 used to track onecomponent over a wide range of frequencies by an adaptive selection of aselected frequency band from among a bank of overlapping frequency bandswithin the signal decomposition function 2302 and the fractional-phaserepresentation function 2303, according to some embodiments of thepresent invention.

FIG. 3.1 is a graph of the wavelet amplitude responses versus frequencyof three wide-band wavelet bands, according to some embodiments of thepresent invention.

FIG. 3.2 is a graph of the wavelet amplitude responses versus frequencyof three narrow-band wavelet bands, according to some embodiments of thepresent invention.

FIG. 4 is a block diagram of a subsystem 2600 used to generate aselection signal used to select one component over a wide range offrequencies, according to some embodiments of the present invention.

FIG. 5 is a block diagram of a subsystem 2700 used to generate aselection signal used to select one component over a wide range offrequencies, according to some embodiments of the present invention.

FIG. 6 is a graph 2800 of the wavelet amplitude responses versusfrequency of about forty-seven wide-band wavelet bands, according tosome embodiments of the present invention.

FIG. 7 is an enlarged portion 2900 of graph 2800 of the waveletamplitude responses versus frequency of a large number of (in this case,about forty-seven) wide-band wavelet bands, according to someembodiments of the present invention.

FIG. 8 is a table 3000 of a number of beats-per-minute heart rates, theassociated center frequency for each and the k_(r) scaling parameter foreach, according to some embodiments of the present invention.

FIG. 9 is a graph 3100 of the real portion 3110 and imaginary portion3120 of a wavelet impulse response, according to some embodiments of thepresent invention.

FIG. 10 is a MATLAB program 3200 used to perform the QP transformationand obtain QP objects, according to some embodiments of the presentinvention.

FIGS. 11.1, 11.2 and 11.3 show three portions of a MATLAB program 3300used to perform the QP transformation and obtain time-interpolated QPobjects, according to some embodiments of the present invention.

FIG. 12 is a MATLAB program 3400 used to collect QP objects into astream, according to some embodiments of the present invention.

FIG. 13 is a MATLAB program 3500 used to track a component of a signal,according to some embodiments of the present invention.

FIG. 14 is a MATLAB program 3600 used to smooth a stream of QPamplitudes, according to some embodiments of the present invention.

FIGS. 15.1 and 15.2 show two portions of a MATLAB program 3700 used totrack a component of a signal based upon a reference center band andguard band, according to some embodiments of the present invention.

FIG. 16 shows examples sequences of QP labels, with an expected sequence3800 and a sequence 3801 with disturbances, according to someembodiments of the present invention.

FIGS. 17.1 and 17.2 show two portions of a MATLAB program 3900 used toperform correction of QP label sequences with disturbances, according tosome embodiments of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Although the following detailed description contains many specifics forthe purpose of illustration, a person of ordinary skill in the art willappreciate that many variations and alterations to the following detailsare within the scope of the invention. Specific examples are used toillustrate particular embodiments; however, the invention described inthe claims is not intended to be limited to only these examples, butrather includes the full scope of the attached claims. Accordingly, thefollowing preferred embodiments of the invention are set forth withoutany loss of generality to, and without imposing limitations upon theclaimed invention.

Further, in the following detailed description of the preferredembodiments, reference is made to the accompanying drawings that form apart hereof, and in which are shown by way of illustration specificembodiments in which the invention may be practiced. It is understoodthat other embodiments may be utilized and structural changes may bemade without departing from the scope of the present invention. Theembodiments shown in the Figures and described here may include featuresthat are not included in all specific embodiments. A particularembodiment may include only a subset of all of the features described,or a particular embodiment may include all of the features described.

Regarding the reference numbers appearing in the Figures—the samereference number is used throughout when referring to an identicalcomponent which appears in multiple Figures. Signals and connections maybe referred to by the same reference number or label, and the actualmeaning will be clear from its use in the context of the description.

For a detailed background description of some embodiments of theinvention, see the handwritten notebook pages of U.S. Provisional PatentApplication No. 61/801,292, filed Mar. 15, 2013, and Appendix A andAppendix B of U.S. Provisional Patent Application 60/656,630, filed Feb.23, 2005, each of which is incorporated herein by reference in itsentirety.

In some embodiments, a bandpass filter bank may be implemented using theShort-Time Fourier Transform (STFT), of which digital forms are wellestablished utilizing the Fast Fourier Transform (FFT) at the website(referenced Mar. 13, 2014)en.wikipedia.org/wiki/Short-time_Fourier_transform.

In some embodiments, more control of the placement of center frequenciesfor the bands is obtained by using the “Chirp-Z Transform” (CZT) inplace of the FFT in forming the STFT. The design criterion for the STFTis the choice of window function w(n), which in turn controls thebandwidth and stopband response of the resulting bandpass filters. Thesedesign choices are well understood in the art, and the considerationstranslate directly to those set forth in this specification and in thepatents incorporated herein by reference.

In some embodiments, the impulse response of a digital bandpass may beexpressed as h(n)=w(n)*exp(−j2πf_(c)nT) where exp(x)=e^(x), j=√−1(square root of minus one), f_(c) is the center frequency in Hz, n is atime-sampling index, and T is the sampling period of the data inseconds. This is a modulated-window form, where w(n) defines a prototypelow-pass filter function, and the complex exponential modulates (shiftsthe frequency response of) the low-pass up so that it is centered not at0 Hz but at fc.

In practice, a bandpass-filtered output signal y(n) is formed through aprocess of convolution between impulse response h(n) and input signalx(n), through a convolution sum: y(n)=Σ_(m) h(m) x(n−m)=Σ_(m) x(m)h(n−m) (i.e., y(n)=sum_over_m(h(m)*x(n−m))=sum_over_m(x(m)*h(n−m))). Forh(n) of finite length, the summation is of finite length for eachcomputed output point at sample index n. Substituting the above-definedh(n) to the above convolution yields a form of the STFT. In someembodiments, the convolution process is performed using frequency-domaintechniques to increase computational efficiency, using, for example,methods such as the “overlap-add” or “overlap-save” methods.

In some embodiments, specification of w(n) for both the STFT and theabove-defined digital bandpass filter controls the bandwidth and generalresponse behavior of the filter, design considerations for which areknown extensively in the art of digital low-pass filter design, as maybe found at website en.wikipedia.org/wiki/Digital_filter, and in thefollowing references:

-   S. K. Mitra, Digital Signal Processing: A Computer-Based Approach,    New York, N.Y.: McGraw-Hill, 1998.-   A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing,    Upper Saddle River, N.J.: Prentice-Hall, 2010. (In Oppenheim &    Shafer, Chapters 6 & 7 cover filter design in detail.)

In some embodiments, the digital bandpass may be implemented based uponwavelets as found in the following reference: The Illustrated WaveletTransform Handbook, Paul S. Addison, Institute of Physics Publishing,2002; particularly as in Chapter 2, per the Morlet Wavelet. While theMorlet Wavelet is formally defined for continuous-time, it may beexpressed in sampled-time form by substituting time variable t with nT,where n is the time-sampling index and T is the sampling intervalexpressed, e.g., in seconds. As such, the Morlet Wavelet is a specialcase of the modulated-window form of the digital bandpass filter above,where w(n) is Gaussian in shape.

As used herein, a wavelet-transform function is sometimes referred to asa wavelet or wavelet transfer function and each has the same meaning asthe other(s); two or more wavelet-transform functions are sometimesreferred to as wavelets, and each has the same meaning as the other(s);a digitized signal is sometimes referred to as signal X, and each hasthe same meaning as the other; a particular frequency component of adecomposed signal x are sometimes referred to as a component, and eachhas the same meaning as the other; bandpass wavelet-transform functionsare sometimes referred to as bandpass wavelets or as bandpasses, andeach has the same meaning as the other(s); a problem is sometimesreferred to as an issue and each has the same meaning as the other; andthe term “without loss of generality” is sometimes abbreviatedw.l.o.g.—and is intended to mean that the preceding discussion is justone example—thus in other embodiments of the invention, other suitableparameters are used.

In some embodiments, the first data structure further includes linkedattributes, including: a descriptor that includes a difference ofabscissa values between the abscissa value included in the particulardata structure and the abscissa value included in a first linked datastructure relative to this particular data structure, a descriptor thatincludes a difference of abscissa values between the abscissa valueincluded in the particular data structure and the abscissa valueincluded in a second linked data structure relative to this particulardata structure, a descriptor that includes an indication of deviationfrom an expected sequence of phase labels, and a descriptor thatincludes a moving average of abscissa values for a group of datastructures surrounding the particular data structure.

FIG. 1.1 is a block diagram of a parallel filter bank 100, in generalimplemented as more fully described in U.S. Pat. No. 7,702,502 thatissued on Apr. 20, 2010 with the title “APPARATUS FOR SIGNALDECOMPOSITION, ANALYSIS AND RECONSTRUCTION”, which is incorporatedherein by reference in its entirety. U.S. Pat. No. 7,702,502 describes amethod of signal decomposition using filter bank 100 having a parallelarrangement of N filter sections that use the Parallel-Form Kovtun-RicciWavelet Transform. In some embodiments, parallel filter bank 100 isimplemented in software, firmware, hardware, and/or combinationsthereof. An original signal x 101 is applied to the input of the bank,and a set of N component signals y₁ . . . y_(N) 104 are provided at theoutputs of the N filter sections (also called “component bands”, “bandfilters” or simply, “bands”) of filter bank 100. In some embodiments,the filter sections are each comprised of a cascade of a componentfilter H and a delay element D, with the component filters havingtransfer functions denoted by H₁ . . . H_(N) 102, and the delay elementshaving transfer functions denoted by D₁ . . . D_(N) 103. The p^(th)filter section 105 of filter bank 100, where p is an integer between 1and N, inclusive, is thus comprised of component filter H_(p) 106 (oneexample of which is discussed further in the below-described FIG. 2) anddelay element D_(p) 107. Original input signal x 101 is provided at theinputs of all filter sections of filter bank 100, each of which producescorresponding stream of values of the component signal y_(p) 108, wherep is an integer between 1 and N, inclusive.

In some embodiments, a fractional-phase determination function generatesa fractional-phase representation of each component signal y_(p) 108.For example, in some embodiments, the fraction is ¼ and the functionsare quarter-phase parameter-determination functions QP₁-QP_(N) 110 thatdetermine four time values (one time value for each “quarter” phase(first zero-crossing to amplitude maximum, amplitude maximum to secondzero-crossing, second zero-crossing to amplitude minimum, and amplitudeminimum to final zero crossing of a single cycle)) and two amplitudevalues (amplitude maximum and amplitude minimum) to generate eachquarter-phase representation objects QP₁-QP_(N) 109; however, otherembodiments can use other fractions. In the embodiment shown, aplurality of streams of quarter-phase representation objects QP₁-QP_(N)109 is output, wherein each stream is a sequential series of successivequarter-phase representation objects QP_(P), each based upon thecorresponding component signal y_(p) 108. Each component signal y_(p)108 and each set of quarter-phase-representation objects QP_(P) areassociated (in some embodiments, implicitly) with the center frequencyof their corresponding band filter H_(P)-D_(P). In some embodiments, thecenter frequency of each filter band is fixed, so it can be difficult toaccurately track a signal (such as a heart beat) that has a wide rangeof possible frequencies, and whose rate can change rapidly.

In some embodiments, the present invention as represented by FIG. 1.1and FIG. 1.2 improves upon the invention of U.S. Pat. No. 7,702,502 byreplacing at least one band filter-and-QP process (e.g., the p^(th)filter-and-QP section 120) with a further parallel bank of filter-and-QPprocesses 2400 (see FIG. 2) whose associated band filters have a closerfrequency spacing than the frequency spacing used by the band filters inparallel filter bank 100. In some embodiments, the p^(th) filter-and-QPsection 120 that is replaced or supplemented by bank 2400 is thatsection for the band designed for the lowest frequency (or fundamentalfrequency, if the fundamental frequency happens not to be the lowestfrequency) component of the initial input signal x 101.

Thus, in contrast to the system described in U.S. Pat. No. 7,702,502,which used one single-band filter for each frequency component and/orfewer than two band center frequencies per octave, the present inventionreplaces at least one component's band filter and QP processing 120 ofFIG. 1.1 (and the corresponding functions 2302 and 2303 described below)with a bank of band filters and associated QP processes (e.g., bank 2400of FIG. 2 described below) and a selector that selects, from among theplurality of QP outputs, that QP output having the strongest signal. Insome embodiments, the sequential series of successive quarter-phaserepresentation objects QP_(P) from that bank includes a frequencyparameter (e.g., an index of the filter band from which the signal wasobtained, or the actual frequency or rate, or some other valuecorresponding to one or more of these parameters) as well as the fourtime values and two amplitude values in the QP objects described in U.S.Pat. No. 7,702,502. In some embodiments, the QP objects of the presentinvention also include other parameters as described in U.S. Pat. No.7,702,502.

FIG. 1.2 is a block diagram of a system 2300. As described more fully inU.S. Pat. No. 7,702,502 (which is incorporated herein by reference inits entirety), in some embodiments, system 2300 includes aninput/analysis process 2301, an interpretive process 2305, astorage/transmission block 2309, and a re-synthesis/output process 2310.In some embodiments, the Input/Analysis Process block 2301 takes theoriginal signal and produces a corresponding stream of objects (in someembodiments, this output includes a plurality of streams of QP objectsincluding a stream of successive quarter-phase representation objectsQP_(P) with frequency parameter(s) from bank 2400 of FIG. 2). In someembodiments, the original signal is applied to the Signal Decompositionblock 2302, the output of which is the set of corresponding componentsignals. These signals are then processed in the Fractional PhaseRepresentation block 2303 to identify the object boundaries and measurebasic attributes, and the corresponding object-related information ispassed to the Object Construction and Linking block 2304 to constructthe object streams, filling out whatever additional object-related, datastructure related information (i.e., attributes, links, etc.) is neededin a particular application. In cases of multiple original signals, theInput/Analysis Process block would be repeated and/or duplicated foreach original signal. The resulting object streams from each Process maythen be merged into a single composite stream of objects.

The Interpretive Process block 2305 takes the object stream and producesan interpretation of the original signal(s). In some embodiments, theState Construction block 2306 takes the object stream and constructsstates from them. The resulting series of states, along with theunderlying objects by which they are defined, then form the input to theOrganized Mapping block 2307, where the information is mapped in statespace and/or a vector space along one or more object attributes. Asstated in the context of this invention, the information may be mappeddirectly in some ad-hoc manner, for example using a sequence detector onthe states and/or some nonlinear, neural and/or fuzzy map formed on theobject attributes. In some embodiments, the information may also be usedfor training a model. Once trained, the information may be applied tothe model to produce a mapped output. In some embodiments, the mappedinformation is then passed to a Pattern Recognition, Discriminationand/or Display block 2308 to transform the mapped information into ahuman-interpretable form, such as for example an automatedidentification and/or diagnosis of a certain condition, and/orvisualization of relevant mapped information. Automated identificationcould involve simple thresholding on the mapped information, or coulduse more sophisticated detection and discrimination techniques such asNovelty Detection and Support Vector Machines. (See The Nature ofStatistical Learning Theory 2^(nd) Edition , by V. Vapnik, Springer 1995; Support-Vector Learning , by C. Cortes and V. Vapnik, 20 MachineLearning 1995 (which are both incorporated herein by reference in theirentirety)).

The Storage/Transmission block 2309 takes the object stream and/or theoriginal signal samples and/or samples of the component signals (or apredetermined select subset of the component signals) and stores some orall of them in memory and/or transmits some or all of them over acommunications link. The Re-synthesis/Output Process block 2310 takesthe object stream from a communications link and/or storage andreconstructs an estimate of the original signal(s). The object streamcorresponding to a desired original signal is recovered from storageand/or received from a communications link via the Retrieval/Receptionblock 2311. Estimates of the component signals for the desired originalsignal are then produced by the Component Reconstruction block 2312, andthe component signal estimates are then combined in the SignalReconstruction block 2313 to produce an estimate of the desired originalsignal. If desired, the individual component signals may be output fromthe Re-synthesis/Output Process block 2310 as well. Multiple originalsignals may be reconstructed using multiple instances of this Process,once for each desired original signal. The reconstructed signal(s) maythen be displayed, for example, on a plot trace (or series of plottraces) for human interpretation, if desired, along with the output ofthe Interpretive Process block 2305.

Adaptive (Controlled) QP Parameters

FIG. 2 is a block diagram of a method for processing QP parameters toobtain adaptive parameters useful for tracking varying frequencycomponents, wherein x=digitized input signal 2401,

-   B₁, B₂, . . . B_(N) =Wavelet filters bank 2412,-   QP₁, QP2, . . . QP_(N)=a bank of quarter-phase generators 2410    corresponding to each frequency band 2406,-   QP₁, QP₂, . . . QP_(N)=a set of streams of quarter-phase parameters    2409 corresponding to each frequency band.

In some embodiments, QP selector 2421 is controlled by a selection(control) signal 2422 and selects, at given point in time, one QP streamas output 2429 from the set of QP streams: QP₁, QP₂ . . . QP_(N).

In some embodiments, selection signal 2422 may indicate the band havingthe maximum power or amplitude from among the bands operating on signalx 2401, where a band having maximum amplitude means one of the bandshaving an amplitude with a magnitude no smaller than the other bands inthe associated bank. (For purposes of generating the selection orindication signal, the terms “maximum-power” and “maximum-amplitude” areto be used interchangeably.) In some embodiments, selection signal 2422may indicate the band 2420 having the maximum power or amplitude fromamong the bands operating on another signal, or in another frequencyrange. In some embodiments, by associating the maximum-amplitude bandindication with the band's center frequency, an estimate of thecomponent frequency is formed, and used as a frequency estimate signal.

The present invention tracks the frequency of a component of a signalx(n), and is well-suited for signals with widely varying fundamentalperiodicities. Consider the case where the fundamental periodicities inquasi-periodic analog signal X (which is digitized to form the initialdigitized input signal x 2401 of FIG. 2) varies over a substantiallywide range, e.g., where the ratio of the highest frequency to the lowestof the periodicity is a factor of two or more. For signal x 2401 that isnot locally sinusoidal, the local TFA (time-frequency analysis) willshow energy at the fundamental frequency f₀(t) and substantially integerharmonics n·f₀(t), where n is an integer, or in general x=Σ_(n)a_(n)(t)·cos(φ_(n)(t)), where a_(n)(t) is the amplitude function of timefor the nth frequency component, and φ_(n)(t) is the corresponding phasefunction.

An example phase function would be φ_(n)(t)=∫q_(n)f(t)dt+φ_(n)(t), wherethe q_(n) denote frequency factors from one component to the next.Typically q_(n) is a monotonically increasing series, and the φ_(n)(t)are representative of the locally static phase relationship from onecomponent to the next. The spacing of the q_(n) for adjacent values of ndenotes the (local) frequency spacing between components.

Note that for determining the rate of a component, in some embodiments,it is preferable for the component output from the wavelet band to belocally sinusoidal, so that the QP sequence is “clean” (i.e., does notexhibit reversals in the sequence ABCD) and does not show significantinterference from neighboring components of x.

The wavelets/bands should be narrow-band sufficiently to emphasize the(rate) component of interest and suppress other components. This can bean issue if the component spacing is narrower than the expected raterange. In this case, for the wavelets to cover the frequency range ofinterest covered by the component, at some frequencies of the component(e.g., lower frequencies of the range), the next-higher component willbe still passed by the wavelet transfer function (frequency response).(Likewise, at higher frequencies of the component range, the next-lowercomponent could be passed by the wavelet.) Interfering neighboringcomponents then appear at the wavelet output, resulting in potentiallysubstantial deviation from a locally sinusoidal wave shape.

Of course, narrowing the wavelet bandwidth results in limited coverageof frequency range for the component, as the wavelet responsesignificantly attenuates the component at the edges of the wavelet band.

This creates difficulty in extracting and/or tracking certain desiredfrequency components of the initial digitized signal x if the desiredcomponent has a wide range of possible frequencies (or rates, expressedfor example in cycles per second), particularly if the signal hasmultiple components spaced at frequency factors narrower than the ratioof the highest to lowest frequency in the frequency range of the desiredcomponent. The present invention provides a solution to this problem.

In some embodiments, the solution that allows resolving of the desiredcomponent from a component set over a substantially wide range offundamental component frequencies consists of replacing a single-bandprocess H_(n) in a bank (e.g., Hp 106 in bank 100 of FIG. 1.1) with abank 2412 (See FIG. 2) of wavelets.

FIG. 3.1 is a graph 2501 of the frequency response (the amplituderesponse) of a wavelet band 2512 with two neighboring bands 2511 (thenext-lower-frequency component band, having a cross-over point 2515 withband 2512) and 2513 (the next-higher-frequency-component band, having across-over point 2516 with band 2512).

In the present invention, each frequency-component band (e.g., 2511,2512 and 2513) processes an initial digitized signal x through a digitalbandpass filter configured to have a center frequency and a bandwidth,each of which is specified by a respective parameter. In someembodiments, each digital bandpass filter is implemented as a softwareroutine and/or hardware circuit that can be executed in parallel orserially with other ones of the digital bandpass filters. In someembodiments, the digital bandpass filters are implemented usingwavelets. In some embodiments, the outputs of the digital bandpassfilters are each sequential streams of digital values denoted as y_(n).In some embodiments, each stream y_(n) of digital values is processed bya respective fractional-phase reduction unit (again, implemented assoftware routines and/or hardware circuits) that reduces the amount ofdata while retaining certain essential characteristics, and outputs astream of digital values denoted as FP_(n). In some embodiments, thefractional-phase reduction unit is implemented as a quarter-phasereduction unit, so each stream y_(n) of digital values is processed by arespective quarter-phase unit (again, these are implemented as softwareroutines and/or hardware circuits) that reduces the amount of data whileretaining certain essential characteristics, and outputs a stream ofdigital values denoted as QP_(n).

In some embodiments, this bank of system and method 2400 of FIG. 2 isdesigned with bandpass wavelets with center frequencies disposed suchthat their responses overlap substantially. In this case, the bands arenot necessarily designed to decompose the signal x 2401 into components(although they could be used for that in other embodiments), but toidentify where in frequency the desired component(s) have significant(dominant) energy (power). The bank 2412 of overlapping bandpasses 2406operating on signal x 2401 will be excited by varying degrees inresponse to a time-local frequency component. The amplitudes of thewavelet outputs y_(n) 2404 may thus be analyzed at each (or certain)points in time to determine the characteristics of x 2401 as a functionof frequency (or with respect to frequency). In some embodiments, theamplitude of the wavelet output may be analyzed at each point in timeand the largest (maximum) found across bands. In some embodiments, thisthen forms the basis for a control selection signal 2422 for selectingthe desired component signal from among the wavelet outputs 2404 or fromamong set of streams of quarter-phase parameters 2409 as described inthe description of FIG. 2. In some embodiments, one band 2420 (e.g., thep^(th) band) includes its respective digital bandpass filter 2406 thatoutputs its stream of wavelet outputs y_(p) 2404 and its respectivequarter-phase measurement unit 2407 that outputs its stream ofquarter-phase objects QP_(p).

In some embodiments, the bandpass ranges (passbands) of the bands ofeach of a plurality of particular bands in wavelet filter bank 2412,relative to that of its closest-neighboring band on either the higher-or lower-frequency side, are such that the cross-over point between oneband and the next is only about −0.1 dB from the maximum response at thecenter frequencies of either of the two bands. In some embodiments, eachband's filter's response at the cross-over point with the neighboring(next) band is no further than about −0.2 dB from the maximum responseat the band's center frequency. In some embodiments, each band'sfilter's response at the cross-over point with the neighboring band isno further than about −0.5 dB from the maximum response at the band'scenter frequency. In some embodiments, each band's filter's response atthe cross-over point with the neighboring band is no further than about−0.75 dB from the maximum response at the band's center frequency. Insome embodiments, each band's filter's response at the cross-over pointwith the neighboring band is no further than about −1 dB from themaximum response at the band's center frequency. In some embodiments,each band's filter's response at the cross-over point with theneighboring band is at least about −1 dB from the maximum response atthe band's center frequency. The “frequency range” of each bandpassfilter's passband is defined as a continuous set of frequenciessurrounding the bandpass filter's center frequency out to thefrequencies at which the response drops below that of the neighboringfilter's passband.

FIG. 3.2 is a graph 2502 the frequency response (the amplitude response)of a wavelet band 2522 with two neighboring bands 2521 (thenext-lower-frequency component band) and 2523 (thenext-higher-frequency-component band). In some embodiments, the filterfor each respective band (2521, 2522, 2523) has the same centerfrequency but a narrower bandwidth than the corresponding wider-bandfilters used to obtain each respective band (2511, 2512, 2513) in graph2501 of FIG. 3.1. In some embodiments, the filter for each respectiveband (2521, 2522, 2523) has center frequencies spaced more narrowly thanthe spacing of the center frequencies of the wider-band filters used toobtain certain bands (2511, 2512, 2513) in graph 2501 of FIG. 3.1.

FIG. 4 is a block diagram of a subsystem 2600 used to generate aselection signal used to select one component over a wide range offrequencies, according to some embodiments of the present invention. Insome embodiments, subsystem 2600 includes a plurality of bandpasswavelet bands 2612, each operating on signal x and producing one or moreband outputs each being a sequence of filtered values y_(n) (bandsignals) that are each analyzed by amplitude determination and selector2621. In some embodiments, amplitude determination and selector 2621determines the amplitude of each of the band signals y_(n) and selectsone of the band signals that is from the band having the maximumamplitude value as determined by amplitude determination and selector2621 without a selection signal; in other embodiments, amplitudedetermination and selector 2621 selects one of the band signals y_(n)that is from the band having some selected value as determined byamplitude determination and selector 2621 based on selection signal2622. In some embodiments, amplitude determination and selector 2621selects a plurality of the band signals y_(n) that are from the bandshaving near to the maximum value as determined by amplitudedetermination and selector 2621 without a selection signal; in otherembodiments, amplitude determination and selector 2621 selects aplurality of the band signals y_(n) that are from those certain selectedbands based on selection signal 2622. In some embodiments, the amplitudeof each of the band signals y_(n) is determined and then smoothed (e.g.,using low-pass filters, moving averages, or the like) before it entersunit 2621.

FIG. 5 is a block diagram of a subsystem 2700 used to generate aselection signal used to select one component over a wide range offrequencies, according to some embodiments of the present invention. Insome embodiments, subsystem 2700 includes a plurality of quarter-phaseamplitude-determination units 2712, each generating one or more streamsof QP values each being a sequence of QP_(n) objects including timevalues as well as quarter-phase amplitude values a_(n) that are eachanalyzed by amplitude determination and selector 2721. In someembodiments, amplitude determination and selector 2721 selects one ofthe sequence of amplitude values a_(n) that is from the band having themaximum value as determined by amplitude determination and selector 2721without a selection signal; in other embodiments, amplitudedetermination and selector 2721 selects one of the sequences ofamplitude values a_(n) that is from the band having some selected valueas determined by amplitude determination and selector 2721 based onselection signal 2722. In some embodiments, amplitude determination andselector 2721 selects a plurality of the filtered sequence of amplitudevalues a_(n) that are from the bands having near to the maximum value asdetermined by amplitude determination and selector 2721 without aselection signal; in other embodiments, amplitude determination andselector 2721 selects a plurality of the plurality of sequences ofamplitude values a_(n) that are from those certain selected bands basedon selection signal 2722. In some embodiments, each of the sequences ofamplitude values a_(n) is smoothed before it enters unit 2721 (e.g.,using low-pass filters, moving averages, or the like).

FIG. 6 is a graph 2800 of the wavelet responses versus frequency ofabout forty-seven wide-band wavelet bands, according to some embodimentsof the present invention. In some embodiments, the main responses 2810include a plurality of bands having mainlobes 2811-2819, and each bandhas a plurality of sidelobes. In some embodiments, the first pluralityof sidelobes 2820 have peaks about −32 dB from the mainlobe responsepeaks, and sidelobes 2821-2829 each correspond to a respective one ofthe mainlobes 2811-2819; the second plurality of sidelobes 2830 havepeaks each about −54 dB from the main response peaks, and sidelobes2831-2839 each correspond to a respective one of the mainlobes2811-2819; the third plurality of sidelobes 2840 have peaks each about−64 dB from the main response peaks, and sidelobes 2841-2849 eachcorrespond to a respective one of the mainlobes 2811-2819; the fourthplurality of sidelobes 2850 have peaks each about −74 dB from the mainresponse peaks, and sidelobes 2851-2859 each correspond to a respectiveone of the mainlobes 2811-2819.

FIG. 7 is an enlarged portion 2900 of graph 2800 of the waveletresponses versus frequency of a large number of (in this case, aboutforty-seven) wide-band wavelet bands, according to some embodiments ofthe present invention. In some such embodiments, one bandpass waveletband 2512 (solid emphasis line) has two neighboring bands: thenext-lower-frequency component band 2511 (long-dashed emphasis line),having a cross-over point 2515 with band 2512, and thenext-higher-frequency-component band 2513 (short-dashed emphasis line),having a cross-over point 2516 with band 2512. In some such embodiments,the cross-over points are less than −0.1 dB from the maximum responsemagnitude.

Graph 2800 shows magnitude frequency response as example of wavelet bankfor adaptive system of FIG. 2 or for control-signal generation of FIG. 4and FIG. 5 described above. Some embodiments of the design usearchitecture described in the descriptions of FIGS. 3.1, 3.2, 4, 5, 6,7, 10 and 11.1-11.3. This an analytic bank, with these responsescorresponding to the real part (the imaginary response are implied byextension). FIG. 7 is a zoomed-in version of the plot of FIG. 6. In bothplots, the X-axis is frequency (Hz) and Y-axis is magnitude (dB). Designparameters for this example are N_(k)=4, N_(m)=4 without loss ofgenerality (sometimes abbreviated as w.l.o.g., this is intended to meanthat in other embodiments of the invention, other suitable parametersare used).

Responses are normalized to have substantially 0 dB (unity gain) at theresponse peak, being the analytic frequency of the wavelet (“actualcenter frequency” 2512.2 per FIG. 3.1). This bank has the centerfrequencies spaced relatively closely—in this example, without loss ofgenerality, approximately a nominal spacing of 18 bands per octave.

In some embodiments, the spacing, in combination with the bandwidths ofthe bandpasses, is chosen such that the responses cross at roughly −0.01dB, generally a small number, so that the analysis representssubstantially high resolution in frequency (along the frequency axis),sufficient to resolve frequency of the underlying component to satisfythe accuracy demanded by the application. For this example, the datasample rate F_(s)=200 Hz without loss of generality.

The table 3000 of FIG. 8 shows values for the wavelets for this examplebank. As the bank is intended, for this example, to resolve a heartrate, the analytic frequencies of the wavelets are chosen to cover arange corresponding to the range of heart rates expected underphysiological conditions (normal rest to exercise), without loss ofgenerality.

The column labeled “R” shows the analytic frequencies in units of beatsper minute (BPM), corresponding to heart rate. The column labeled f_(A)shows the same analytic frequencies of units of Hz (Hertz, or cycles persecond). The column k_(r) shows the values of k_(r) for each waveletbandpass of this example bank. The values are chosen to be even toensure integer delays in the system. Values of N_(W) for each band areset to k_(r)/2 in this example bank. This provides example bank as perbank 2400 of FIG. 2 or bank 2600 of FIG. 5 or bank 2700 of FIG. 6.

For input signal x, the bank performs an analysis whereby components inx will excite the bands to varying degrees. Periodicities in x closestto certain bands will excite them the most, so they are expected to havethe largest local amplitude.

FIG. 9 is a plot 3100 of an example impulse response L_(K) (analytic) ofband as per the description in U.S. Pat. No. 7,702,502, which issued onApr. 20, 2010 titled “APPARATUS FOR SIGNAL DECOMPOSITION, ANALYSIS ANDRECONSTRUCTION,” and which is incorporated herein by reference. Trace3110 is the real part of the impulse response; the imaginary part istrace 3120. The Y-axis is the impulse-response coefficient; the X-axisis the true index in samples. This response corresponds to thelowest-frequency band (r=1, k_(r)=200 in the list 3000 of FIG. 8) of theexample bank, without loss of generality.

Other bands would be scaled versions of this response according towavelet principles well-understood in the art and established also inAppendix A of the inventor's U.S. Provisional Patent Application60/656,630, filed Feb. 23, 2005, titled “SYSTEM AND METHOD FOR SIGNALDECOMPOSITION, ANALYSIS AND RECONSTRUCTION,” and U.S. Pat. No.7,702,502, which claimed benefit of U.S. Provisional Patent Application60/656,630, both of which are incorporated herein by reference in itsentirety.

Flow of Processing Example

Referring to FIG. 2, Input signal x 2401 is operated on in parallel bythe wavelets 2406 in the bank 2412. The respective analytic outputs 2404are then used by respective QP operators 2410 to form a set offractional-phase representations 2409 of each (in some embodiments, aquarter-phase representation is formed, without loss of generality).

FIG. 10 is a listing of MATLAB code 3200 to implement QP transformationfrom analytic wavelet output y_(n) (passed in is an input argument xhere). Output is sequence of QP object stream information: Lqp is astream of QP labels (encoding A, B, C, D here as 1, 2, 3, and 4,respectively) so that each element of vector Lqp is single sequential QPobject label. Similarly, output iqp is the time index of each of the QPobjects (in sample indexing into vector x). Output aqp is thecorresponding stream of QP object amplitudes, such that each element ofaqp vector corresponds to the instantaneous amplitude of analytic signalx at corresponding QP point iqp.

FIG. 11 (which includes FIG. 11.1, FIG. 11.2, and FIG. 11.3 takentogether) is a listing of MATLAB code 3300 to implement QPtransformation similarly to that of function 3200 shown in FIG. 10except that the values of iqp and aqp are interpolated at the QP pointsof argument x (y_(n)). Specifically, at the appropriate zero-crossings,the x-intercept is solved for, providing a more accurate measure of iqp.Using a linear model is accurate in practice because near X=0, sin(X)=X.

Correspondingly, the value of aqp is linearly interpolated at themore-accurate value of iqp. Higher-order interpolations or fits cancertainly be considered as part of this invention as they are wellunderstood in the art. (For both functions 3200 and 3300 of FIG. 10 andFIG. 11, output argument Msem is a placeholder and is not implemented orused in this embodiment.)

In some embodiments, if one considers the transform of signal x 2401 (asdescribed above for FIG. 2, FIG. 5 and FIG. 6) as the parallel waveletoperation resulting in the series of signals y_(n), n=1 . . . N, we canconstruct matrix Y as the appending of signals y_(n), each a beingcolumn, appended column-wise. We assume here, without loss ofgenerality, that the intrinsic delays of the wavelets in the banks arecompensated so that the outputs are time-aligned (as described on p. 78of Appendix A in U.S. Provisional Patent Application 60/656,630, filedFeb. 23, 2005, titled “SYSTEM AND METHOD FOR SIGNAL DECOMPOSITION,ANALYSIS AND RECONSTRUCTION,” which is incorporated herein by referencein its entirety). We can then operate on matrix Y to produce the QPtransformation. The code 3400 in FIG. 34 does this by repetitively(iteratively) calling either function getCmpQp( ) or functiongetCmpQpItp( ) on each column of Y. (Y is passed in here as inputargument X.)

Output sObj is a structure array (an array of structs). Each element ofsObj is itself a structure containing fields Lqp, iqp, and aqp, the QPobject stream data as output by the functions 3200 shown in FIG. 10 or3300 of FIG. 11.1, FIG. 11.2, and FIG. 11.3. Array sObj is indexed bythe band, so that the nth element sObj(n) contains the QP information(corresponding to signal y_(n)), of the set of signals Y_(n), n=1 . . .M.

The code 3500 (function) in FIG. 13 performs the processing to resolvethe desired component by maximum instantaneous amplitude. It works byadvancing time until a wavelet output encounters a QP transition, thenupdates the “state” accordingly. The “state” here is considered as avertical linking as described/contemplated in Book 1 pages 3-8 inAppendix A of the inventor's U.S. Provisional Patent Application60/656,630, and FIGS. 7A, 7B, 7C, and 7D and their description in U.S.Pat. No. 7,702,502, which claimed benefit of U.S. Provisional PatentApplication 60/656,630, both of which are incorporated herein byreference in their entirety. So, for sake of this example embodiment,vertical linking occurs across band index ib indexing sObj(ib). At eachstate update, the maximum-amplitude band is found and the correspondingQP information is stored in vector abmx, imbx, Lbmx and ixqp. Thesevectors are then stored as fields at the end into output structuresQpCmp.

In code 3500 of FIG. 13:

-   abmx=amplitude of highest-amplitude wavelet at state nqp;-   ibmx=band index corresponding to abmx;-   Lbmx=QP label corresponding to abmx;-   ixqp=time index of original signal at corresponding state updates;    and-   sQpCmp.aqp, sQpCmp.Lqp, and sQpCmp.iqp=QP parameters of desired    components (dominant comp.) over frequency band covered by wavelet    bank.

For some types of signals x, the energy is very pulsatile, for examplewith ECG signals, such that the signal has a large crest factor. Beingquasi-periodic, the signal is thus very “spiky” in its waveshape. Thiscan cause ambiguity in the wavelet output amplitude—where thehigher-frequency wavelets are excited more during the spike that duringthe dwell time. (“Ripples” in the amplitude sequence aqp for the higherfrequency wavelets.) This causes biases in the selection of the bandbased upon amplitude, where the band selection gets skewed upward duringthe time locally surrounding the “spikes.”

In one embodiment, the solution would be to increase the order N_(K) ofthe derivative band of the wavelets. Other embodiments would seek toprocess the amplitude sequence aqp to remove/suppress the ripples of aqpdue to the input spikes.

The function flpsQpA.m 3600 in FIG. 36 performs smoothing (low-passfiltering) of the sequences sObj(ib).aqp. In this embodiment anintegral-kernel wavelet operates on the aqp sequence corresponding toeach ib^(th) band. The integral-kernel wavelet smoother is as peroperator hq( ) page 66 of Book 1 in Appendix A of the inventor's U.S.Provisional Patent Application 60/656,630, and FIGS. 7A, 7B, 7C, and 7Dand their description in U.S. Pat. No. 7,702,502, which claimed benefitof U.S. Provisional Patent Application 60/656,630, both of which areincorporated herein by reference in their entirety, with N_(o) herecorresponding to N_(m) on p. 66 of Book 1 and wQP here corresponding toN_(W) for hq as per p. 66 of Book 1. Scale wQP is scaled to correspondto a nominal time, though in some embodiments it may be a constant withrespect to band number. Here the “fixed-time” scaling is accomplishedthrough input argument T (in seconds) along with analytic (center)frequency parameter vector fan (in Hz) for each band. Thus wQP is avector, in units of number of quarter-phases approximating time T foreach band. Operator No is the order, and is arbitrary (usually a nominalvalue of No=2 is used). Output aqpm is the smoothed amp (amplitude)sequence and stored back to sObj as a new field for each correspondingband. The new smoothed amplitude sequence may then be used forestimating the center of a narrower band range over which to track thedesired component.

The function trkMxQpAGrd 3700 (MATLAB code) in FIGS. 15.1-15.2implements modified tracking, it operates similar to the code 3500 inFIG. 13, except it first identifies a band range using aqpm, at eachstate update, before then finding the max of aqp over that restrictedband range.

The state of aqpm is stored on state variable aqpmSt and the state ofaqp is stored in state variable aqpSt. The resulting tracked componentinformation is output as before, with additional tracked informationfrom aqpm output in second output structure as sQpCmpm. As before incode 3500 in FIG. 13, the desired component QP information is covered instructure sQpCmp fields aqp, ibqp, and iqp and this forms the “QPstream” for this component.

FIG. 16 shows example QP streams 3800. The resulting QP stream 3801 canin some embodiments contain repeated labels 3810 for many consecutivestate updates, sometimes interspersed with “phase reversals” 3820(reversed in the expected forward pattern of labels).

The code 3900 in FIGS. 17.1-17.2 works to both collect all repeats intoa single QP of that label, and to also remove phase reversals.Collection of repeats deletes and collapses the label repeat and takesan amplitude-weighted average of the indices (both time and bandindices) and an average of the amplitude for each epoch of sequentialrepeated labels. The result is a cleaned sequence of QP objects, usefulfor further analysis, storage, or reconstruction as per all of Book 1 inAppendix A of the inventor's U.S. Provisional Patent Application60/656,630, and pp. 1-20 of Appendix B of the inventor's U.S.Provisional Patent Application 60/656,630.

In some embodiments, the present invention provides an apparatus 2400that includes: a computer having a storage device; a source of aninitial series of digitized signal values; a first plurality ofdigital-bandpass filters 2412 each operably coupled to the source ofdigitized signal values and each configured to digitally filter theinitial series of digitized signal values, wherein each one of the firstplurality of digital-bandpass filters has a respective center frequencythat is unique among respective center frequencies of the firstplurality of digital-bandpass filters and a respective frequency rangethat overlaps the respective frequency range of a closest neighboringone of the first plurality of digital-bandpass filters, and wherein eachone of the first plurality of digital-bandpass filters has an outputsignal 2402; a first plurality of quarter-phase measurement units 2410that each determines a plurality of amplitude values and at least fourphase-determined time points 2409 per full waveform cycle of the outputsignal of each one of the first plurality of digital bandpass filters;and a first frequency-component tracker 2421 that uses the outputsignals from the plurality of quarter-phase measurement units to detectand track a first frequency component as that first tracked frequencycomponent changes from being primarily within the respective frequencyrange of a first one of the first plurality of digital-bandpass filtersto being primarily within the respective frequency range of a second oneof the first plurality of digital-bandpass filters.

In some embodiments of apparatus 2400, each one of the first pluralityof digital-bandpass filters includes a wavelet-transform filter.

In some embodiments of apparatus 2400, the first frequency-componenttracker 2421 further includes: an output quarter-phase measurement unitthat determines at least two amplitude values and at least fourphase-determined time points per full waveform cycle of the firsttracked frequency component, and that outputs a first series ofrespective data structures that each indicates the at least twoamplitude values, the at least four phase-determined time points perrespective full waveform cycle of the first tracked frequency component,and a per-cycle instantaneous frequency of the first tracked frequencycomponent for the respective full waveform cycle of the first trackedfrequency component.

In some embodiments of apparatus 2400, each one of the first pluralityof digital-bandpass filters 2412 is a wavelet-transform filter; and thefirst frequency-component tracker further includes: a firstquarter-phase maximum-amplitude determination unit that determines whichone of the first plurality of quarter-phase measurement units had amaximum amplitude value no lower than did any other one of the firstplurality of quarter-phase measurement units during a time period andthat outputs a selection signal based on the determination; and a firstselector that selects information from at least one of first pluralityof quarter-phase measurement units based on the selection signal, andoutputs the selected information and an indication of frequency from thecorresponding at least one of the first plurality of digital-bandpassfilters.

Some embodiments of apparatus 2400 further include: a second pluralityof digital-bandpass filters, wherein each one of the second plurality ofdigital-bandpass filters has a center frequency that is unique among thesecond plurality of digital-bandpass filters, wherein each one of thesecond plurality of digital-bandpass filters is a wavelet-transformfilter, and wherein each one of the second plurality of digital-bandpassfilters has an output signal; a second plurality of quarter-phasemeasurement units operatively coupled to receive the output signals fromthe second plurality of digital-bandpass filters, wherein each of thesecond plurality of quarter-phase measurement units determines andoutputs at least two amplitude values and at least four phase-determinedtime points per full waveform cycle of a corresponding one of the secondplurality of digital-bandpass filters; wherein each one of the firstplurality of digital-bandpass filters is a wavelet-transform filter; andwherein the first frequency-component tracker further includes: aquarter-phase maximum-amplitude determination unit that determines whichone of the first plurality of quarter-phase measurement units had amaximum amplitude value no lower than did any other one of the firstplurality of quarter-phase measurement units during a time period andthat outputs a selection signal based on the determination; and aselector that selects information from at least one of second pluralityof quarter-phase measurement units based on the selection signal, andoutputs the selected information and an indication of a frequency of thefirst tracked frequency component.

In some embodiments of apparatus 2400, the first frequency-componenttracker outputs a series of data structures each containing aquarter-phase label (Lqp), an interpolated quarter-phase index value(iqp), and an interpolated quarter-phase amplitude value (aqp) of thetracked frequency component.

In some embodiments of apparatus 2400, the first frequency-componenttracker further includes an interpolator that interpolates azero-crossing time value to find a quarter-phase index value (iqp) ofanalytic signal x of the initial series of digitized signal values.

In some embodiments of apparatus 2400, the first frequency-componenttracker further includes an interpolator that interpolates aquarter-phase index value (iqp) and a quarter-phase amplitude value(aqp) at QP points of analytic signal x of the initial series ofdigitized signal values.

In some embodiments, the present invention provides an apparatus 2400that includes: digitally filtering an initial series of digitized signalvalues in a computer to generate a first plurality of digitally bandpassfiltered signals, wherein each one of the first plurality of digitallybandpass filtered signals has a respective center frequency that isunique among respective center frequencies of the first plurality ofdigitally bandpass filtered signals and a respective frequency rangethat overlaps the respective frequency range of a closest neighboringone of the first plurality of digitally bandpass filtered signals;determining a first plurality of quarter-phase amplitude values andquarter-phase-determined time points per full waveform cycle of each oneof the first plurality of digitally bandpass filtered signals; using thefirst plurality of quarter-phase amplitude values for detecting andtracking, in the computer, a first tracked frequency component as thatfirst tracked frequency component changes from being primarily withinthe respective frequency range of a first one of the first plurality ofdigitally bandpass filtered signals to being primarily within therespective frequency range of a second one of the first plurality ofdigitally bandpass filtered signals; and storing information regardingthe tracked frequency component into a storage device.

In some embodiments of method 2400, the digitally filtering of theinitial series of digitized signal values to generate the firstplurality of digitally bandpass filtered signals further includesfiltering the initial series of digitized signal values to generate aplurality of wavelet-transformed signals, based on a wavelet from awavelet transform.

In some embodiments of method 2400, the using of the first plurality ofquarter-phase amplitude values for detecting and tracking the firstfrequency component further includes: determining at least two amplitudevalues and at least four phase-determined time points per full waveformcycle of the first tracked frequency component, and outputting a firstseries of respective data structures that each indicates the at leasttwo amplitude values, the at least four phase-determined time points perrespective full waveform cycle of the first tracked frequency component,and a per-cycle frequency of the first tracked frequency component forthe respective full waveform cycle of the first tracked frequencycomponent.

In some embodiments of method 2400, the digitally filtering to generatethe first plurality of digitally bandpass filtered signals includesfiltering the initial series of digitized signal values to generate aplurality of wavelet-transformed signals, based on a wavelet from awavelet transform, and the using of the first plurality of quarter-phaseamplitude values for detecting and tracking the first tracked frequencycomponent further includes: determining which one of the first pluralityof quarter-phase measurement units had a maximum amplitude value nolower than did any other one of the first plurality of quarter-phasemeasurement units during a time period and that outputs a selectionsignal based on the determination; and selecting information from atleast one of first plurality of quarter-phase amplitude values and thefirst plurality of quarter-phase-determined time points based on theselection signal, and outputting the selected information and anindication of frequency from the corresponding at least one of the firstplurality of digitally bandpass filtered signals.

Some embodiments of method 2400 further include digitally filtering theinitial series of digitized signal values in a computer to generate asecond plurality of digitally wavelet-transformed signals based on awavelet from a wavelet transform, wherein each one of the secondplurality of digitally bandpass filtered signals has a respective centerfrequency that is unique among respective center frequencies of thesecond plurality of digitally bandpass filtered signals and a respectivefrequency range that overlaps the respective frequency range of aclosest neighboring one of the second plurality of digitally bandpassfiltered signals; determining a second plurality of quarter-phaseamplitude values and quarter-phase-determined time points per fullwaveform cycle of each corresponding one of the second plurality ofdigitally bandpass filtered signals; wherein the digitally filtering togenerate the first plurality of digitally bandpass filtered signalsincludes filtering the initial series of digitized signal values togenerate a plurality of wavelet-transformed signals based on a waveletfrom a wavelet transform, and wherein the using of the first pluralityof quarter-phase amplitude values for detecting and tracking the firsttracked frequency component further includes: determining which one ofthe first plurality of quarter-phase amplitude values andquarter-phase-determined time points had a maximum amplitude value nolower than did any other one of the first plurality of quarter-phaseamplitude values and quarter-phase-determined time points during a timeperiod and outputting a selection signal based on the determination; andselecting information from at least one of second plurality ofquarter-phase amplitude values and quarter-phase-determined time pointsbased on the selection signal, and outputting the selected informationand an indication of frequency from the corresponding at least one ofthe second plurality of digitally bandpass filtered signals.

Some embodiments of method 2400 further include outputting a series ofdata structures each containing a quarter-phase label (Lqp), aninterpolated quarter-phase index value (iqp), and an interpolatedquarter-phase amplitude value (aqp) of the tracked frequency component.

Some embodiments of method 2400 further include interpolating azero-crossing time value to find a quarter-phase index value (iqp) ofanalytic signal x of the initial series of digitized signal values.

Some embodiments of method 2400 further include interpolating aquarter-phase index value (iqp) and a quarter-phase amplitude value(aqp) at QP points of analytic signal x of the initial series ofdigitized signal values.

In some embodiments, the present invention provides a non-transitorycomputer-readable storage medium having instructions stored thereon,wherein the instructions, when executed by a suitably programmedcomputer, perform a method 2400 that includes: digitally filtering aninitial series of digitized signal values in a computer to generate afirst plurality of digitally bandpass filtered signals, wherein each oneof the first plurality of digitally bandpass filtered signals has arespective center frequency that is unique among respective centerfrequencies of the first plurality of digitally bandpass filteredsignals and a respective frequency range that overlaps the respectivefrequency range of a closest neighboring one of the first plurality ofdigitally bandpass filtered signals; determining a first plurality ofquarter-phase amplitude values and quarter-phase-determined time pointsper full waveform cycle of each one of the first plurality of digitallybandpass filtered signals; using the first plurality of quarter-phaseamplitude values for detecting and tracking, in the computer, a firsttracked frequency component as that first tracked frequency componentchanges from being primarily within the respective frequency range of afirst one of the first plurality of digitally bandpass filtered signalsto being primarily within the respective frequency range of a second oneof the first plurality of digitally bandpass filtered signals; andstoring information regarding the tracked frequency component into astorage device.

In some embodiments of the computer-readable storage medium havinginstructions to execute method 2400, the digitally filtering includeswavelet-transforming the initial series of digitized signal values togenerate a plurality of wavelet-transformed signals.

Some embodiments of the computer-readable storage medium havinginstructions to execute method 2400 include further instructions that,when executed by a suitably programmed computer, cause the digitallyfiltering of the initial series of digitized signal values to generatethe first plurality of digitally bandpass filtered signals to furtherinclude filtering the initial series of digitized signal values togenerate a plurality of wavelet-transformed signals, based on a waveletfrom a wavelet transform.

Some embodiments of the computer-readable storage medium havinginstructions to execute method 2400 include further instructions that,when executed by a suitably programmed computer, cause the using of thefirst plurality of quarter-phase amplitude values for detecting andtracking the first frequency component to further include: determiningat least two amplitude values and at least four phase-determined timepoints per full waveform cycle of the first tracked frequency component,and outputting a first series of respective data structures that eachindicates the at least two amplitude values, the at least fourphase-determined time points per respective full waveform cycle of thefirst tracked frequency component, and a per-cycle frequency of thefirst tracked frequency component for the respective full waveform cycleof the first tracked frequency component.

Some embodiments of the computer-readable storage medium havinginstructions to execute method 2400 include further instructions that,when executed by a suitably programmed computer, cause the digitallyfiltering to generate the first plurality of digitally bandpass filteredsignals to further include filtering the initial series of digitizedsignal values to generate a plurality of wavelet-transformed signals,based on a wavelet from a wavelet transform, and wherein the using ofthe first plurality of quarter-phase amplitude values for detecting andtracking the first tracked frequency component further includes:determining which one of the first plurality of quarter-phasemeasurement units had a maximum amplitude value no lower than did anyother one of the first plurality of quarter-phase measurement unitsduring a time period and that outputs a selection signal based on thedetermination; and selecting information from at least one of firstplurality of quarter-phase amplitude values and the first plurality ofquarter-phase-determined time points based on the selection signal, andoutputting the selected information and an indication of frequency fromthe corresponding at least one of the first plurality of digitallybandpass filtered signals.

Some embodiments of the computer-readable storage medium havinginstructions to execute method 2400 include further instructions that,when executed by the suitably programmed computer, cause the method tofurther include: digitally filtering the initial series of digitizedsignal values in a computer to generate a second plurality of digitallywavelet-transformed signals based on a wavelet from a wavelet transform,wherein each one of the second plurality of digitally bandpass filteredsignals has a respective center frequency that is unique amongrespective center frequencies of the second plurality of digitallybandpass filtered signals and a respective frequency range that overlapsthe respective frequency range of a closest neighboring one of thesecond plurality of digitally bandpass filtered signals; determining asecond plurality of quarter-phase amplitude values andquarter-phase-determined time points per full waveform cycle of eachcorresponding one of the second plurality of digitally bandpass filteredsignals; wherein the digitally filtering to generate the first pluralityof digitally bandpass filtered signals includes filtering the initialseries of digitized signal values to generate a plurality ofwavelet-transformed signals based on a wavelet from a wavelet transform,and wherein the using of the first plurality of quarter-phase amplitudevalues for detecting and tracking the first tracked frequency componentfurther includes: determining which one of the first plurality ofquarter-phase amplitude values and quarter-phase-determined time pointshad a maximum amplitude value no lower than did any other one of thefirst plurality of quarter-phase amplitude values andquarter-phase-determined time points during a time period and outputtinga selection signal based on the determination; and selecting informationfrom at least one of second plurality of quarter-phase amplitude valuesand quarter-phase-determined time points based on the selection signal,and outputting the selected information and an indication of frequencyfrom the corresponding at least one of the second plurality of digitallybandpass filtered signals.

Some embodiments of the computer-readable storage medium havinginstructions to execute method 2400 include further instructions that,when executed by a suitably programmed computer, cause the method tofurther include: outputting a series of data structures each containinga quarter-phase label (Lqp), an interpolated quarter-phase index value(iqp), and an interpolated quarter-phase amplitude value (aqp) of thetracked frequency component.

In some embodiments, the present invention provides an apparatus thatincludes: a computer having a storage device; means for digitallyfiltering an initial series of digitized signal values in a computer togenerate a first plurality of digitally bandpass filtered signals,wherein each one of the first plurality of digitally bandpass filteredsignals has a respective center frequency that is unique amongrespective center frequencies of the first plurality of digitallybandpass filtered signals and a respective frequency range that overlapsthe respective frequency range of a closest neighboring one of the firstplurality of digitally bandpass filtered signals; means for determininga first plurality of quarter-phase amplitude values andquarter-phase-determined time points per full waveform cycle of each oneof the first plurality of digitally bandpass filtered signals; means forusing the first plurality of quarter-phase amplitude values fordetecting and tracking, in the computer, a first tracked frequencycomponent as that first tracked frequency component changes from beingprimarily within the respective frequency range of a first one of thefirst plurality of digitally bandpass filtered signals to beingprimarily within the respective frequency range of a second one of thefirst plurality of digitally bandpass filtered signals; and means forstoring information regarding the tracked frequency component into astorage device.

It is to be understood that the above description is intended to beillustrative, and not restrictive. Although numerous characteristics andadvantages of various embodiments as described herein have been setforth in the foregoing description, together with details of thestructure and function of various embodiments, many other embodimentsand changes to details will be apparent to those of skill in the artupon reviewing the above description. The scope of the invention shouldbe, therefore, determined with reference to the appended claims, alongwith the full scope of equivalents to which such claims are entitled. Inthe appended claims, the terms “including” and “in which” are used asthe plain-English equivalents of the respective terms “comprising” and“wherein,” respectively. Moreover, the terms “first,” “second,” and“third,” etc., are used merely as labels, and are not intended to imposenumerical requirements on their objects.

What is claimed is:
 1. An apparatus comprising: a computer system havinga storage device; a source of an initial series of digitized signalvalues; a first plurality of digital-bandpass filters each operablycoupled to the source of digitized signal values and each configured todigitally filter the initial series of digitized signal values, whereineach one of the first plurality of digital-bandpass filters has arespective center frequency that is unique among respective centerfrequencies of the first plurality of digital-bandpass filters and arespective frequency range that overlaps the respective frequency rangeof a closest neighboring one of the first plurality of digital-bandpassfilters, and wherein each one of the first plurality of digital-bandpassfilters has an output signal; a first plurality of quarter-phasemeasurement units implemented by software and circuitry in the computersystem that each determines a plurality of amplitude values and at leastfour phase-determined time points per full waveform cycle of the outputsignal of a corresponding one of the first plurality of digital bandpassfilters; and a first frequency-component tracker implemented by softwareand circuitry in the computer system that uses the output signals fromthe plurality of quarter-phase measurement units to detect and track afirst frequency component as that first tracked frequency componentchanges from being primarily within the respective frequency range of afirst one of the first plurality of digital-bandpass filters to beingprimarily within the respective frequency range of a second one of thefirst plurality of digital-bandpass filters.
 2. The apparatus of claim1, wherein each one of the first plurality of digital-bandpass filtersincludes a wavelet-transform filter.
 3. The apparatus of claim 1,wherein the first frequency-component tracker further includes: anoutput quarter-phase measurement unit that determines at least twoamplitude values and at least four phase-determined time points per fullwaveform cycle of the first tracked frequency component, and thatoutputs a first series of respective data structures that each indicatesthe at least two amplitude values, the at least four phase-determinedtime points per respective full waveform cycle of the first trackedfrequency component, and a per-cycle instantaneous frequency of thefirst tracked frequency component for the respective full waveform cycleof the first tracked frequency component.
 4. The apparatus of claim 1,wherein each one of the first plurality of digital-bandpass filters is awavelet-transform filter; and wherein the first frequency-componenttracker further includes: a first quarter-phase maximum-amplitudedetermination unit that determines which one of the first plurality ofquarter-phase measurement units had a maximum amplitude value with amagnitude no smaller than did any other one of the first plurality ofquarter-phase measurement units during a time period and that outputs aselection signal based on the determination; and a first selector thatselects information from at least one of first plurality ofquarter-phase measurement units based on the selection signal, andoutputs the selected information and an indication of frequency from thecorresponding at least one of the first plurality of digital-bandpassfilters.
 5. The apparatus of claim 1, further comprising: a secondplurality of digital-bandpass filters, wherein each one of the secondplurality of digital-bandpass filters has a center frequency that isunique among the second plurality of digital-bandpass filters, whereineach one of the second plurality of digital-bandpass filters is awavelet-transform filter, and wherein each one of the second pluralityof digital-bandpass filters has an output signal; a second plurality ofquarter-phase measurement units operatively coupled to receive theoutput signals from the second plurality of digital-bandpass filters,wherein each of the second plurality of quarter-phase measurement unitsdetermines and outputs at least two amplitude values and at least fourphase-determined time points per full waveform cycle of a correspondingone of the second plurality of digital-bandpass filters; wherein eachone of the first plurality of digital-bandpass filters is awavelet-transform filter; and wherein the first frequency-componenttracker further includes: a quarter-phase maximum-amplitudedetermination unit that determines which one of the first plurality ofquarter-phase measurement units had a maximum amplitude value with amagnitude no smaller than did any other one of the first plurality ofquarter-phase measurement units during a time period and that outputs aselection signal based on the determination; and a selector that selectsinformation from at least one of second plurality of quarter-phasemeasurement units based on the selection signal, and outputs theselected information and an indication of a frequency of the firsttracked frequency component.
 6. The apparatus of claim 1, wherein thefirst frequency-component tracker outputs a series of data structureseach containing a quarter-phase label (Lqp), an interpolatedquarter-phase index value (iqp), and an interpolated quarter-phaseamplitude value (aqp) of the tracked frequency component.
 7. Theapparatus of claim 1, wherein the first plurality of quarter-phasemeasurement units each further includes: an interpolator thatinterpolates a quarter-phase index value (iqp) and a quarter-phaseamplitude value (aqp) at QP points of the output signal of thecorresponding one of the first plurality of digital bandpass filters. 8.A computer-implemented method comprising: digitally filtering an initialseries of digitized signal values in a computer system to generate afirst plurality of digitally bandpass filtered signals, wherein each oneof the first plurality of digitally bandpass filtered signals has arespective center frequency that is unique among respective centerfrequencies of the first plurality of digitally bandpass filteredsignals and a respective frequency range that overlaps the respectivefrequency range of a closest neighboring one of the first plurality ofdigitally bandpass filtered signals; determining, with software andcircuitry in the computer system, a first plurality of quarter-phaseamplitude values and quarter-phase-determined time points per fullwaveform cycle of each one of the first plurality of digitally bandpassfiltered signals; using the first plurality of quarter-phase amplitudevalues for detecting and tracking, with software and circuitry in thecomputer system, a first tracked frequency component as that firsttracked frequency component changes from being primarily within therespective frequency range of a first one of the first plurality ofdigitally bandpass filtered signals to being primarily within therespective frequency range of a second one of the first plurality ofdigitally bandpass filtered signals; and storing information regardingthe tracked frequency component into a storage device.
 9. Thecomputer-implemented method of claim 8, wherein the digitally filteringof the initial series of digitized signal values to generate the firstplurality of digitally bandpass filtered signals further includesfiltering the initial series of digitized signal values to generate aplurality of wavelet-transformed signals, based on a wavelet from awavelet transform.
 10. The computer-implemented method of claim 8,wherein the using of the first plurality of quarter-phase amplitudevalues for detecting and tracking the first frequency component furtherincludes: determining at least two amplitude values and at least fourphase-determined time points per full waveform cycle of the firsttracked frequency component, and outputting a first series of respectivedata structures that each indicates the at least two amplitude values,the at least four phase-determined time points per respective fullwaveform cycle of the first tracked frequency component, and a per-cyclefrequency of the first tracked frequency component for the respectivefull waveform cycle of the first tracked frequency component.
 11. Thecomputer-implemented method of claim 8, wherein the digitally filteringto generate the first plurality of digitally bandpass filtered signalsincludes filtering the initial series of digitized signal values togenerate a plurality of wavelet-transformed signals, based on a waveletfrom a wavelet transform, and wherein the using of the first pluralityof quarter-phase amplitude values for detecting and tracking the firsttracked frequency component further includes: determining which one ofthe first plurality of quarter-phase measurement units had a maximumamplitude value with a magnitude no smaller than did any other one ofthe first plurality of quarter-phase measurement units during a timeperiod and that outputs a selection signal based on the determination;and selecting information from at least one of first plurality ofquarter-phase amplitude values and the first plurality ofquarter-phase-determined time points based on the selection signal, andoutputting the selected information and an indication of frequency fromthe corresponding at least one of the first plurality of digitallybandpass filtered signals.
 12. The computer-implemented method of claim8, further comprising: digitally filtering the initial series ofdigitized signal values in a computer to generate a second plurality ofdigitally wavelet-transformed signals based on a wavelet from a wavelettransform, wherein each one of the second plurality of digitallybandpass filtered signals has a respective center frequency that isunique among respective center frequencies of the second plurality ofdigitally bandpass filtered signals and a respective frequency rangethat overlaps the respective frequency range of a closest neighboringone of the second plurality of digitally bandpass filtered signals;determining a second plurality of quarter-phase amplitude values andquarter-phase-determined time points per full waveform cycle of eachcorresponding one of the second plurality of digitally bandpass filteredsignals; wherein the digitally filtering to generate the first pluralityof digitally bandpass filtered signals includes filtering the initialseries of digitized signal values to generate a plurality ofwavelet-transformed signals based on a wavelet from a wavelet transform,and wherein the using of the first plurality of quarter-phase amplitudevalues for detecting and tracking the first tracked frequency componentfurther includes: determining which one of the first plurality ofquarter-phase amplitude values and quarter-phase-determined time pointshad a maximum amplitude value with a magnitude no smaller than did anyother one of the first plurality of quarter-phase amplitude values andquarter-phase-determined time points during a time period and outputtinga selection signal based on the determination; and selecting informationfrom at least one of second plurality of quarter-phase amplitude valuesand quarter-phase-determined time points based on the selection signal,and outputting the selected information and an indication of frequencyfrom the corresponding at least one of the second plurality of digitallybandpass filtered signals.
 13. The computer-implemented method of claim8, further comprising: outputting a series of data structures eachcontaining a quarter-phase label (Lqp), an interpolated quarter-phaseindex value (iqp), and an interpolated quarter-phase amplitude value(aqp) of the tracked frequency component.
 14. The computer-implementedmethod of claim 8, further comprising: interpolating a quarter-phaseindex value (iqp) and a quarter-phase amplitude value (aqp) at QP pointsof a corresponding one of the first plurality of digitally bandpassfiltered signals.
 15. A non-transitory computer-readable storage mediumhaving instructions stored thereon, wherein the instructions, whenexecuted by a suitably programmed computer system, perform a methodcomprising: digitally filtering an initial series of digitized signalvalues in the computer system to generate a first plurality of digitallybandpass filtered signals, wherein each one of the first plurality ofdigitally bandpass filtered signals has a respective center frequencythat is unique among respective center frequencies of the firstplurality of digitally bandpass filtered signals and a respectivefrequency range that overlaps the respective frequency range of aclosest neighboring one of the first plurality of digitally bandpassfiltered signals; determining, with software and circuitry in thecomputer system, a first plurality of quarter-phase amplitude values andquarter-phase-determined time points per full waveform cycle of each oneof the first plurality of digitally bandpass filtered signals; using thefirst plurality of quarter-phase amplitude values for detecting andtracking, with software and circuitry in the computer system, a firsttracked frequency component as that first tracked frequency componentchanges from being primarily within the respective frequency range of afirst one of the first plurality of digitally bandpass filtered signalsto being primarily within the respective frequency range of a second oneof the first plurality of digitally bandpass filtered signals; andstoring information regarding the tracked frequency component into astorage device.
 16. The computer-readable storage medium of claim 15,having further instructions stored thereon, wherein the furtherinstructions, when executed by a suitably programmed computer, cause thedigitally filtering of the initial series of digitized signal values togenerate the first plurality of digitally bandpass filtered signals tofurther include filtering the initial series of digitized signal valuesto generate a plurality of wavelet-transformed signals, based on awavelet from a wavelet transform.
 17. The computer-readable storagemedium of claim 15, having further instructions stored thereon, whereinthe further instructions, when executed by a suitably programmedcomputer, cause the using of the first plurality of quarter-phaseamplitude values for detecting and tracking the first frequencycomponent to further include: determining at least two amplitude valuesand at least four phase-determined time points per full waveform cycleof the first tracked frequency component, and outputting a first seriesof respective data structures that each indicates the at least twoamplitude values, the at least four phase-determined time points perrespective full waveform cycle of the first tracked frequency component,and a per-cycle frequency of the first tracked frequency component forthe respective full waveform cycle of the first tracked frequencycomponent.
 18. The computer-readable storage medium of claim 15, havingfurther instructions stored thereon, wherein the further instructions,when executed by a suitably programmed computer, cause the digitallyfiltering to generate the first plurality of digitally bandpass filteredsignals to further include filtering the initial series of digitizedsignal values to generate a plurality of wavelet-transformed signals,based on a wavelet from a wavelet transform, and wherein the using ofthe first plurality of quarter-phase amplitude values for detecting andtracking the first tracked frequency component further includes:determining which one of the first plurality of quarter-phasemeasurement units had a maximum amplitude value with a magnitude nosmaller than did any other one of the first plurality of quarter-phasemeasurement units during a time period and that outputs a selectionsignal based on the determination; and selecting information from atleast one of first plurality of quarter-phase amplitude values and thefirst plurality of quarter-phase-determined time points based on theselection signal, and outputting the selected information and anindication of frequency from the corresponding at least one of the firstplurality of digitally bandpass filtered signals.
 19. Thecomputer-readable storage medium of claim 15, having furtherinstructions stored thereon, wherein the further instructions, whenexecuted by a suitably programmed computer, cause the method to furtherinclude: digitally filtering the initial series of digitized signalvalues in a computer to generate a second plurality of digitallywavelet-transformed signals based on a wavelet from a wavelet transform,wherein each one of the second plurality of digitally bandpass filteredsignals has a respective center frequency that is unique amongrespective center frequencies of the second plurality of digitallybandpass filtered signals and a respective frequency range that overlapsthe respective frequency range of a closest neighboring one of thesecond plurality of digitally bandpass filtered signals; determining asecond plurality of quarter-phase amplitude values andquarter-phase-determined time points per full waveform cycle of eachcorresponding one of the second plurality of digitally bandpass filteredsignals; wherein the digitally filtering to generate the first pluralityof digitally bandpass filtered signals includes filtering the initialseries of digitized signal values to generate a plurality ofwavelet-transformed signals based on a wavelet from a wavelet transform,and wherein the using of the first plurality of quarter-phase amplitudevalues for detecting and tracking the first tracked frequency componentfurther includes: determining which one of the first plurality ofquarter-phase amplitude values and quarter-phase-determined time pointshad a maximum amplitude value with a magnitude no smaller than did anyother one of the first plurality of quarter-phase amplitude values andquarter-phase-determined time points during a time period and outputtinga selection signal based on the determination; and selecting informationfrom at least one of second plurality of quarter-phase amplitude valuesand quarter-phase-determined time points based on the selection signal,and outputting the selected information and an indication of frequencyfrom the corresponding at least one of the second plurality of digitallybandpass filtered signals.
 20. The computer-readable storage medium ofclaim 15, having further instructions stored thereon, wherein thefurther instructions, when executed by a suitably programmed computer,cause the method to further include: outputting a series of datastructures each containing a quarter-phase label (Lqp), an interpolatedquarter-phase index value (iqp), and an interpolated quarter-phaseamplitude value (aqp) of the tracked frequency component.